Very nilpotent basis and \(n\)-tuples in Borel subalgebras (Q627740)

Let \({\mathfrak g}\) be a Lie algebra defined over an algebraically closed field of characteristic zero. A vector space basis \(B\) of \({\mathfrak g}\) is called very nilpotent if all the iterated brackets of elements of \(B\) are nilpotent. The author proves that \({\mathfrak g}\) has a very nilpotent basis if and only if \({\mathfrak g}\) is nilpotent. This is a refinement of Engel`s Theorem.